Let x 1,x 2,… be independent identically distributed (i.i.d.) random variables, in which x n=0 or 1 and the probability of ｛x n=1｝ is p. Here p is unknown. Let τ be any finite stopping ...Let x 1,x 2,… be independent identically distributed (i.i.d.) random variables, in which x n=0 or 1 and the probability of ｛x n=1｝ is p. Here p is unknown. Let τ be any finite stopping time for (x n,n1). For any sequential sample (x 1,x 2,…,x τ ) and γ∈(0,1), we have given an optimal confidence limit of p with confidence level γ . Some related problems are also discussed.展开更多
On the basis of strict mathematical description about Failure_Free Period Life Test (FFPLT), the statistical properties of the tests and optimal confidence limit of the parameter are discussed in detail and correspond...On the basis of strict mathematical description about Failure_Free Period Life Test (FFPLT), the statistical properties of the tests and optimal confidence limit of the parameter are discussed in detail and corresponding calculating formulae are found out.展开更多
A renewable component with exponential failure and repair times is considered, and its instantaneous availability at time t is denoted by A（t）. This paper proposes two methods for constructing lower confidence limit...A renewable component with exponential failure and repair times is considered, and its instantaneous availability at time t is denoted by A（t）. This paper proposes two methods for constructing lower confidence limits of A（t） with Chebyshev inequation and generalized p-value approach.展开更多
Stress-strength model is a basic and important tool for reliability analysis.There are few methods to assess the confidence limit of interference reliability when the distribution parameters of stress and strength are...Stress-strength model is a basic and important tool for reliability analysis.There are few methods to assess the confidence limit of interference reliability when the distribution parameters of stress and strength are all unknown.A new assessment method of interference reliability is proposed and the estimates of the distribution parameters are accordingly given.The lower confidence limit of interference reliability with given confidence can be obtained with the method even though the parameters are all unknown.Simulation studies and an engineering application are conducted to validate the method,which suggest that the method provides precise estimates even for sample size of approximately.展开更多
The log-Weibull distribution is a variant of the three-parameter Weibull distribution. The probability plot of a distribution model is desired since it can help to decide on whether the model is appropriate for fittin...The log-Weibull distribution is a variant of the three-parameter Weibull distribution. The probability plot of a distribution model is desired since it can help to decide on whether the model is appropriate for fitting a given dataset and can provide the initial estimate of the model parameters. The decision on the appropriateness of a distribution is somehow subjective. This paper presents a probability plot of the log-Weibull distribution(LWPP). The distribution of the probability plot correlation coefficient is studied. From this distribution, a lower confidence limit is determined for determining whether the probability plot correlation coefficient derived from a given data set is large enough. The appropriateness and usefulness of this study are illustrated by two real-world examples.展开更多
A machine, or other type of 'system' , can often be divided into several subsystems (components)and these subsystems again can be divided into sevreral subsystems (second generation). This process forms a sy...A machine, or other type of 'system' , can often be divided into several subsystems (components)and these subsystems again can be divided into sevreral subsystems (second generation). This process forms a system tree. To assess the reliability of the machine based on data from the trials of components of the machine, virtual system method is employed. It is proved in the paper that the lower confident limit of the reliability of the machine set by the virtual system method is level consistent and asymptotically optimal while the one set by Lindstrom-Maddens method is not.展开更多
文摘Let x 1,x 2,… be independent identically distributed (i.i.d.) random variables, in which x n=0 or 1 and the probability of ｛x n=1｝ is p. Here p is unknown. Let τ be any finite stopping time for (x n,n1). For any sequential sample (x 1,x 2,…,x τ ) and γ∈(0,1), we have given an optimal confidence limit of p with confidence level γ . Some related problems are also discussed.
文摘On the basis of strict mathematical description about Failure_Free Period Life Test (FFPLT), the statistical properties of the tests and optimal confidence limit of the parameter are discussed in detail and corresponding calculating formulae are found out.
文摘A renewable component with exponential failure and repair times is considered, and its instantaneous availability at time t is denoted by A（t）. This paper proposes two methods for constructing lower confidence limits of A（t） with Chebyshev inequation and generalized p-value approach.
文摘Stress-strength model is a basic and important tool for reliability analysis.There are few methods to assess the confidence limit of interference reliability when the distribution parameters of stress and strength are all unknown.A new assessment method of interference reliability is proposed and the estimates of the distribution parameters are accordingly given.The lower confidence limit of interference reliability with given confidence can be obtained with the method even though the parameters are all unknown.Simulation studies and an engineering application are conducted to validate the method,which suggest that the method provides precise estimates even for sample size of approximately.
基金the National Natural Science Foundation of China(No.71371035)
文摘The log-Weibull distribution is a variant of the three-parameter Weibull distribution. The probability plot of a distribution model is desired since it can help to decide on whether the model is appropriate for fitting a given dataset and can provide the initial estimate of the model parameters. The decision on the appropriateness of a distribution is somehow subjective. This paper presents a probability plot of the log-Weibull distribution(LWPP). The distribution of the probability plot correlation coefficient is studied. From this distribution, a lower confidence limit is determined for determining whether the probability plot correlation coefficient derived from a given data set is large enough. The appropriateness and usefulness of this study are illustrated by two real-world examples.
文摘A machine, or other type of 'system' , can often be divided into several subsystems (components)and these subsystems again can be divided into sevreral subsystems (second generation). This process forms a system tree. To assess the reliability of the machine based on data from the trials of components of the machine, virtual system method is employed. It is proved in the paper that the lower confident limit of the reliability of the machine set by the virtual system method is level consistent and asymptotically optimal while the one set by Lindstrom-Maddens method is not.
